"Quadratic Equation of One Variable" PPT courseware 7

Description

"Quadratic Equation of One Variable" PPT courseware 7

Do it

Estimating solutions to quadratic equations

x²+(x+7)²＝11² i.e. x²+7x = 36

Can you find x? How to estimate x?

Can you guess the approximate range of values ​​for x?

Is it possible that X is less than or equal to 0? Tell us your reasons.

Is it possible that X is greater than or equal to 11? Tell us your reasons.

Therefore, the approximate range of x values ​​is: 0

Practice in class

Observe the following equation:

10²+11²+12²＝13²+14²

Can you find five other consecutive integers such that the sum of the squares of the first three numbers is equal to the sum of the squares of the last two numbers?

If the first number among five consecutive integers is x, then the following four numbers can be expressed as: _____, _____, _____, _____.

According to the meaning of the question, the equation can be obtained:

X²+(X+1)²+(X+2)²＝(X+3)²+(X+4)²

That is x²-8x-20=0.

Can you find out what these five integers are?

Summary and expansion

What new knowledge did you learn in this lesson?

Learned the method of estimating the approximate solution of the quadratic equation ax²+bx+c=0 (a, b, c are constants, a≠0);

Know the estimation steps:

Determine the approximate scope first;

Then calculate the value and gradually approach it.

Think about it, is there a convenient way to find the unknown numbers in the equation?

Concluding message

Using equations (systems of equations) to solve related practical problems is an important mathematical idea - the idea of ​​equations.

The quadratic equation is also an effective mathematical model to describe the real world.

sublimation of knowledge

According to the meaning of the question, list the equations and estimate the solutions to the equations:

1. A rectangular nursery with an area of ​​120m2 is 2m longer than its width. What are the length and width of the nursery?

Solution: Assume the width of the rectangle is xm, then the length is (x+2) m. According to the question, we get:

x (x+2) =120.

That is, x²＋2x-120 =0.

According to the meaning of the question, the value range of x is roughly 0

2. A diver performs 10m platform diving training. Under normal circumstances, the athlete must complete the prescribed somersault action before 5m from the water surface, and adjust the posture of entering the water, otherwise it is easy to make mistakes. Assume that the athlete’s movement time after taking off is t (s) and the height h (m) of the athlete from the water surface satisfy the relationship: h=10+2.5t-5t². Then how long does it take him to complete the prescribed action at most.

Solution: According to the question, 5=10+2.5t-5t². That is, 2t² - t-2=0.

According to the meaning of the question, the value range of t is roughly 0

It can be seen from this that the range of t that can make the value of 2t²-t-2 be 0 is 1.2

Keywords: quadratic equation teaching courseware, Qingdao edition ninth grade mathematics volume PPT courseware download, ninth grade mathematics slide courseware download, quadratic equation PPT courseware download, .PPT format;

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Update Time: 2024-10-07

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

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